Operational Formulation of General Relativity as a Quantum Theory, Via the Geometric Spectral Stability Principle

In this work, we present a unified formulation of General Relativity as a Quantum Theory (GRQT), demonstrating that its initial apparent fragmentation stems from the explicit absence of a common operational language, rather than conceptual inconsistencies. We show that by treating spacetime as a discrete causal sampling lattice, geometry can be formally reinterpreted as a discrete dynamic system amenable to spectral analysis. In this context, the Geometric Spectral Stability Principle (GSSP), emerges as the universal criterion for physical admissibility, selecting only the spectrally stable modes of the associated geometric operator. From this perspective, particles are identified as normalizable eigenmodes of the geometric filter defined by causal connectivity, and their masses correspond to eigenvalues fixed by spectral stability. We systematically reinterpret the results obtained in Volumes VI through VIII of GRQT, showing that the classification of particles as topological defects, the derivation of leptonic masses and the fine-structure constant, as well as precision corrections of the $g\!-\!2$ type and cosmological regimes, are distinct manifestations of the same underlying spectral mechanism. The explicit operational translation between discrete geometry and spectral operators eliminates the ambiguity between analogy and derivation, conferring an operationally closed and structurally consistent character to the theory. Thus, quantization is not introduced as an external postulate but emerges directly from the geometric structure of spacetime itself, establishing GRQT as a coherent, finite, and unifying formulation of relativistic and quantum dynamics.